Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty

TL;DR

This paper introduces three deep learning-based metamodeling frameworks that effectively predict nonlinear stochastic dynamic structural responses under combined load and parameter uncertainties, validated on two complex structural case studies.

Contribution

It develops novel neural network architectures combining feature extraction and LSTM with uncertainty quantification, addressing a gap in modeling combined uncertainties in structural systems.

Findings

All models achieved low prediction errors.

MLP-LSTM was most accurate for simpler systems.

MPNN-LSTM and AE-LSTM performed better on complex models.

Abstract

Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters. Studies have successfully incorporated uncertainties related to external loads from natural hazards, but few have simultaneously addressed loading and parameter uncertainties within structural systems while accounting for prediction uncertainty of neural networks. To address these gaps, three metamodeling frameworks were formulated, each coupling a feature-extraction module implemented through a multi-layer perceptron (MLP), a message-passing neural network (MPNN), or an autoencoder (AE) with a long short-term memory (LSTM) network using Monte Carlo dropout and a negative log-likelihood loss. The resulting architectures (MLP-LSTM, MPNN-LSTM, and AE-LSTM) were validated on two case studies: a multi-degree-of-freedom Bouc-Wen system and a 37-story fiber-discretized nonlinear steel moment-resisting frame, both subjected to stochastic seismic excitation and structural parameter uncertainty. All three approaches achieved low prediction errors: the MLP-LSTM yielded the most accurate results for the lower-dimensional Bouc-Wen system, whereas the MPNN-LSTM and AE-LSTM provided superior performance on the more complex steel-frame model. Moreover, a consistent correlation between predictive variance and actual error confirms the suitability of these frameworks for active-learning strategies and for assessing model confidence in structural response predictions.